Stability and dynamic behaviour of bi-directional functionally graded beam subjected to variable axial load

Abstract

The current study emphasizes static stability and dynamic characteristics of bi-directional functionally graded beams subjected to variable axial loads using the Ritz method and Reddy’s beam theory. The material property is varied as a function of the gradation pattern along with the length and thickness directions. The solutions procedures are tested against the results in the literature to show the accuracy of the present method. The influence of uniform, linear, and parabolic axial loads along the length of the beam on buckling and vibration responses are investigated. There is a remarkable variation observed in both the responses, by changing the material properties from isotropic to bi-direction functionally graded. Furthermore, the study reveals that higher stiffness is achieved by the material gradation index increment along the thickness direction compared to the lengthwise gradation index increment. Even the variations in the aspect ratios and end conditions are depicting significant variations in the buckling and vibration responses. Buckling and free vibration modes are also highly sensitive to the nature of variable axial loads and gradation index.